Combinatorics II – Spring 2017
Instructor: Shubhangi Saraf
Timing: MTh 12 pm - 1:20 pm
Office hours: Thursday 1:20 pm– 2:20 pm (Hill 426, Busch Campus)
Text: There is no text, but there are several books that we will be referring to, and many of them will be on library reserve.
Some of the relevant books include: The Probabilistic Method (Alon & Spencer), Extremal Combinatorics (Stasys Jukna), Linear Algebra Methods in Combinatorics (Babai & Frankl)
Prerequisites: 16:642:582 or permission of instructor
Description: This is the second part of a two-semester course surveying basic topics in combinatorics.
Topics for the full year should include most of:
• Enumeration (basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics)
• Matching theory, polyhedral and fractional issues
• Partially ordered sets and lattices, Mobius functions
• Theory of finite sets, hypergraphs, combinatorial discrepancy, Ramsey theory, correlation inequalities
• Probabilistic methods
• Algebraic and Fourier methods • Entropy methods
Grade: The grade will be based on problem sets. There will be about 4 -5 problem sets assigned over the course of the semester. There will be no exams.